Equivalent source distribution for efficient 3‐D acoustic wave equation modeling in the Laplace domain

Abstract

Since the recent introduction of the Laplace‐domain full waveform inversion, an efficient and accurate modeling technique for the 3‐D Laplace‐domain wave equation has been sought. The Laplace‐domain wave equation can be solved on a coarse grid because the field is not propagating. However, it is not possible to accurately compute the Laplace‐domain response by assuming that the source and the receivers are located at the grid nodes when we use a coarse‐grid. To resolve this problem, we propose an equivalent source distribution algorithm that allows us to simulate the free surface condition accurately using a coarse‐grid finite‐element or finite‐difference method. The equivalent source vector obtained from a homogeneous half space model can be used for arbitrarily complex models. Numerical tests show that our algorithm is better than the Kaiser windowed sinc function method in the Laplace domain. Our technique for solving the 3‐D Laplace‐domain wave equation can significantly reduce the computational time required for the modeling.